In an experiment to determine the factors affecting tensile strength in steel plates, the tensilestrength (in kg/mm?), the manganese content (in parts per thousand), and the thickness (inmm) were measured for a sample of 20 plates. The following MINITAB output presents theresults of fitting the model Tensile strength = Bo + B1 Manganese + B2 Thickness.The regression equation isStrength = 26.641 + 3.3201 Manganese – 0.4249 ThicknessPredictorCoef StDevтConstant26.6412.723409.78 0.000Manganese 3.32010.33198 10.00 0.000Thickness -0.42490.12606 -3.37 0.004S = 0.8228 R-Sq = 86.2% R-Sq(adj) =84.6%Analysis of VarianceSourceDFMSRegressionResidual Error 1711.508 0.67692 72.0136.00553.190.000Total1983.517 Find a 95% confidence interval for the coefficient of Manganese.b.a.Find a 99% confidence interval for the coefficient of Thickness.Can you conclude that B1 > 3? Perform the appropriate hypothesis test.d.Can you conclude that B2 < -0.1? Perform the appropriate hypothesis test.C.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Fifty matched pairs of magnitude/depth measurements randomly selected from 10,594 earthquakes recorded in one year from a location in southern California. Find the best predicted depth of an earthquake with a magnitude of 2.2. Use a significance level of 0.05. : Click the icon to view the earthquake measurements. Click here to view the critical values of the Pearson correlation coefficient, r. The regression equation is y = ? + ?x. 回-ト i Critical Values of the Pearson Correlation Coefficient r (Round to one decimal place as needed.) Critical Values of the Pearson Correlation Coefficient r α= 0.05 0.950 0.878 0.811 0.754 0.707 0.666 0.632 0.602 0.576 a = 0.01 0.990 0.959 0.917 0.875 0.834 0.798 0.765 0.735 0.708 NOTE: To test Ho: p=0 Jagainst H,: p#0, reject H, if the absolute value of r is greater than the critical value in the table. 5 10 11 12
The accompanying table lists overhead widths (cm) of seals measured from photographs and the weights (kg) of the seals. Find the (a) explained variation, (b) unexplained variation, and (c) prediction interval for an overhead width of 8.9 cm using a 99% confidence level. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. Click the icon to view the seal data. a. The explained variation is (Round to the nearest integer as needed.) b. The unexplained variation is. (Round to the nearest integer as needed.) c. The 99% prediction interval for an overhead width of 8.9 cm is kg
A linear regression model based on a random sample of 36 observations on the response variable and 4 predictors has a multiple coefficient of determination equal to 0.697. What is the value of the adjusted multiple coefficient of determination?
A study was conducted to determine the relationship between starting salaries (RM thousands) for recent statistics graduates and their grade point averages in the major course. A linear regression model was fitted to the data and the estimates regression function was obtained. Part of the computer output for the above analysis is given below: ANOVA Model Sum of df Mean F Sig. Squares Square Regression 147.28 .000 Error 734.9 40.828 Total 6748.2 Coefficients Unstandardized Coefficients Model Sig. Std. B Error Constant GPA -8.42 3.007 3.395 0.2477 -2.48 12.14 0.011 0.000 (a) Complete the ANOVA table (blue boxes). (b) Write down the estimated regression function. Interpret the estimated parameters. (c) Test whether there is a linear association between salaries and grade point average. Use a = 0.05. (d) Determine the coefficient of determination for the model and interpret its meaning.
A researcher wants to make an equation that will predict a person's support for domestic surveillance from a variety of demographic characteristics (e.g., age, income). What method will they use? A) Multiple regression B) Correlation C) Two-factor ANOVA D) One-sample t-test
A Bivariate Regression was conducted to evaluate the predictive relationship between total years of schooling and annual income. The results of the regression model were F(1,88) = 4.1, p < .05. What can be concluded about these results? Group of answer choices total years of schooling is a significant predictor of annual income. total years of schooling is not a significant predictor of annual income.
In a sample of cars reviewed by Motor Trend magazine, the mean horsepower (hp) was 150 hp with a standard deviation of 36 hp. The mean weight (lbs) was 2500 lbs with a standard deviation of 720 lbs. Assume the relationship between weight and horsepower is linear and has a correlation of r = +0.55. What is the slope of the linear regression model predicting weight (y-variable) from horsepower (x-variable)? 9 13 15 11
The table below lists measured amounts of redshift and the distances (billions of light-years) to randomly selected astronomical objects. There is sufficient evidence to support a claim of a linear correlation, so it is reasonable to use the regression equation when making predictions. For the prediction interval, use a 90% confidence level with a redshift of 0.0126. Find the explained variation. Redshift Distance OA, 0.157904 OB. 0.444904 OC. 0.000582 OD. 0.219582 0.0231 0.34 0.0536 0.76 0.0715 0.99 0.0391 0.56 0.0438 0.63 0.0109 0.15
e) Perform the F Test making sure to state the null and alternative hypothesis.
A linear regression model based on a random sample of 36 observations on the response variable and 4 predictors has a multiple coefficient of determination equal to 0.697. What is the value of the adjusted multiple coefficient of determination?
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There is a dataset of size n = 51 and is for the 50 states and the District of Columbia in the United States. The dependent variable is year 2002 birth rate per 1000 females 18 to 19 years old and independent variable is the violent crime rate (per 1000 population). A simple linear regression model is run with the results given below. What is the Pearson correlation coefficient between x and y variables? The R squared of the model? What kind of relationship there is?

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